Question

7. A firm’s stock sells at $40. The price will be either $35 or $47 three months from now. Assume the risk-free rate is 12% per annum with continuous compounding. a) What is the call price with a strike price of $43 and a maturity of 3 months? b) What is the put price with a strike price of $43 and a maturity of 3 months?

Answer 1

1.
=(Probability of upmove*Call payoff in case of upmove+Probability of downmove*Call payoff in case of downmove)*e^(-rt)
=((e^(12%*3/12)-47/40)/(35/40-47/40)*MAX(47-43,0)+(1-(e^(12%*3/12)-47/40)/(35/40-47/40))*MAX(35-43,0))*e^(-12%*3/12)
=1.87031336

2.
=Call price+X*e^(-rt)-S
=1.87031336+43*e^(-12%*3/12)-40
=3.59947130